Sometimes people say that water is re/9 vib xa(5 p,)qfqwswmoved from clothes in a spin dryer by centrifugal force throwing the water qbi5) fsx,w/vpa q(w9outward. What is wrong with this statement?

Will the acceleration of a car be the same when the w94;xht nh di6+dh*iicar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spe ;h6ht didxnw9hi+*i4 ed? Explain.

Suppose a car moves at constant speed along a hilly road. Where d-c u6zuwn4k ickn-ksl 3)t()noes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretchln-(tzksn - c6kunwu i)k c)43 near the bottom of a hill?

Describe all the forces actwo*v7j3 h7:uy rw4 q5tq tgjn)ing on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the 3j *qrgh 4:5wqj 7vowt7ytu)nchild?

A bucket of water can be whirled in a vertical circle without the watr9f u9u/qo 6v+e(clw uer spilling out, even at the top of the circle when the bucket is upsf9(6/ luvo uc9er+uwq ide down. Explain.

How many “accelerators” do you have in your car? Thwa7yk x1r;t;zere are at least three controls in the car which can be used to cause the car to accelerate. What are theyxkry;wa;z71 t? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hillcxr08o 3 md+ei, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and te308o xdm+cri he sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rouspxid,s c(j( 1l pk2n4nding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang8z of wppx*r zmab;,:;le given i;ppa *zmr o z,w:8bfx;ts speed and radius of the turn?

A girl is whirling a ball on a f2hu.ro5 +uiostring around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball wio5uf r h2.io+ull hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earthl 1gi5 uh1nz2cds h-1kzm8 ov9? If so, how large a force? Consider ani1m1d5 olcs gvu-z2k hh8 91zn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’fi x*nxo3:zh0/ ;drbi;;uvo ss orbit beo3 fho;v*s /x:x; ndbiuz; r0i different?

Which pulls harder graqvz h;m2,ya20oyx 0ly vitationally, the Earth on the Moon, or the Moon on the Earth? yha2 2 ly,oy;00qmzxv Which accelerates more?

The Sun's gravitational pull of-vy q4:e4das(sz 5 ugmhmy,4n the Earth is much larger than the Moon's. Yet the Moon's is mainfyv: z5um4 ss(ad4yg4qem h -,ly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at thul7l2zwlau.d 05+ f cee poles? What two effects are at work? Do lw2ld0 c+uz lf7u.ae5they oppose each other?

The gravitational force on the Moon due to the Eakmr:25 kvtb8 zrth is only about half the force on the Moon due to tbvm 5rktk82: zhe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around iz(+iyh 2-hr8g 3wwl( l)vj1pks*vt sthe Sun larger or smaller than the centripwjw ykhil*pv3il )+- 2z(1tgsh vrs8(etal acceleration of the Earth?

Would it require less speed to launch a satelliio2p: vzb7o zv1 jp( 9 cc/b73yjvqpq8te (a) toward the east or (b) toward the west? Considjc3jv7p:zop2 (v1v/8 o9y zibb7 cqpq er the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a pz;d5idrmwz e,1gr)7n4 i lv0moving elevator: when the elevator (a) accelerates downwardmzd51 ,ii)7 en 0 rprd;w4gvzl, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods inro-+zsgz* l. w outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the fozlw+-.o sg z*rrce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experience-wr0; 5gp3xna *c m w7fcgqvi0s “free fall” or “apparent weightlessness” between s mn50*v-wgfaw q;xgrc0c7 ip3teps.

The Earth moves faster ivt.. 19x+i bk69 n*pazbiakg ewp7b9dn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [N9i. n+ bd1w at 76x*pbbzp9v .kakig9eote: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discor ej (zi-2qz0qvered to have a moon. Explain how this discovjqqi z- ze(20rery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much r bjr--wf w7h7larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from 7w --fwjrr7hb the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19l m7j. 1,hfc 8aydcdg0 tal5e780 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eartjc8zrb5d-b5 n3 s/pk/3*fzl ) bxxxgvh in its orbit around the Sun, and the net force exerted on the Earth. What exertszcdvfjpg - 3xk bz 5/b n5xxbls*)r38/ this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg disdubybpm(a -zu sz3 mm(1/sb2)cus as it rotates uniformly in a horizontup z)db3(m (ss2-yazbm b/ mu1al circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, aa*bobt )zve/:nd circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational aczb /t*a)bvo:e celeration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on-1o o .w7t0wozf7c lvn the edge of a potter’s wheel turning at 45 rpmcfonl o7. 0zov1 wt7w- (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at aq3vua a lm7i6) shfd+* uniform rate in a vertical circle of radius 726sv3 u7)liq aaf+md *h.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum t vtf-z57367yayx fhlspeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independen5x67- yfa tt 7f3hvyzlt of the mass of the car?   

  How large must the coefficient of static friction be between the bq2 o 9o)3)ld;kkxlk dtires and the road if a car is to round a level curve ofd3dk;)) bxlko o q2k9l radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is des j 7o;-jvdxu7ligned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast d lxjo j;7vu-7is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from tg ch7w.o 8+6usj0zav whe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of statiozcwvgw0h6 auj. 8+ s7c friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upl /kx.fubj; d czeo zj/(hwwz-0y+,p/side down at the top of aj,/fjdwz(ye+k z/.z /lc-h 0 ;xowbup circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 xb fh6i6ojd yb4v3 lgv*/ 2nb)kg (including the driver) crosses the rounded top of a hill (rai23b*vx/d h6 jvfl o4yb)gn6bdius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris whee 6jh*j* k. a(vyydiys1l need to make for the passenge h*yi6 akjy1*(y sj.dvrs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirlgak(cm )2 wb.med in a vertical circle of radius 1.10 m. At the lowest point of its motmk(gc ).ab2mwion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a panmz+;i:;va,4 :b2 v9r w yyp t6ukaejxrticle 9.00 cm from the axis of rota imta :rn:y4v+ vu z,kw;b6p29;xyaejtion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ars zl; qhftz.-t0 (efr-e rotated in a cylindrically walled "room." (See z( f se-lht;fzrt-q .0Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotatju-.fpn,nz mzs6lw2 +ed in a circle on a frictionless air-hockey tabletop, and is held in th ,+mu2.pnn jl-zfwsz6is orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the;mwf n lyy-dljeq0r +o/373ab v* q1pp weight of the ball which revolvd; lmo v3 na1jf e0 q+*yb7w-p3ry/lpqes on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelingma/ t: b creaoq;y51ynpy *5a9 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses ii9;.0cvmq o2 .zwdh f$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at jcn6y0 w0yz. *ltzwk43ee:zz 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exertt1w2cz(l0zfk-hiy/ zo2ij7u ed on the car (by the ground) in Example 5-8 when its s1j-kh / i2c(0fiy2t zwozuz7lpeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelert q8.va:j.mo/z0f wx l 3e6r jxd4vjg:ates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway thrv vj4a. :fxr .3 /:low806dtgzejxmqjough the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2oxmg;gk 6 r //w- *hbq9/ejwop.90 m . At a particular instant, its accelerao 6;h prb*9xo-ew g//g /kqjmwtion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Eart tgh7+ yo q(zo0bhz+d8h’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass z+zthg+qhd0y 7 8obo(is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magn97jr qae)qsq4nyp / 6witude of 12 m/s9 )nqewqy p/r6s4a7 jq$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radi yzadr;52/t qyzv/ 0xaus is 1.7vad0tq;a2 yy/ r/5zz x4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the samevn09(y(tq1zqdjh5 ) a tnoyf; mass. What is the accjqd9 nt (tvo);ayhz5y qf1 0n(eleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the s-q-c8 j+ykgsfjv.cn0./ ucbfame radius. What is g +cs/c -bfv0 q.gyj -.fnkcuj8near its surface?   

  Two objects attract each other gravitationally witm5 /t; 1izd)upp9 bn pj -01jyq1srlewh a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of grav w6etk3ooxaqama e lw (n839(u 0x*;uuity, at (a) 3200 m3o(x(m 6 tq80;luaw*aukwa o3uexe n9    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a po y rte33ia i+q*wn9i.jint outside the Earth where thegravitational 9q3n*awii3 .yjr+teiacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivkzy uz6+r k:e4e times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mons4zrky6+e:k zu ter.    $\times10^12$

  A typical white-dwarf star, which once was an average star uu2lpb+45f ;z bjoe: hlike our Sun but is now in thhu 52+jze ;blf: b4poue last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitiun: 41r4oir aesk gm6,ng in the space shuttle. You1irknaor:s, 4 m 4gu6er friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the :ptzp0 +9fp.yct oqq0jh*.e q corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otherey. tt9pq z*ch+0f opq :p0jq. three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sg5m3:nj)p oyceq;u/(v)m,j( mosfojun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumiomyjn,/ vmo5jg:3fp()so)cm e; jq (ung all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the accel5ly-)rj7f y g.i jw yvj/v21oaeration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400jj7ar- gy5/ 2v1w vyj)l i.fyo km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known 8n44l yxhzgu w*kyd oq9 39r*) q u4cne-;reztvalue for the period of the Earth and its distance from the Sun. [Note: 39 n9y)nocq uztl44w e;z*egx-dk4q h*ry 8 urCompare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboy*k9gv5tt0bhml i7x(s , ks/snh/ 8 mput the Earth at a hei (95kl*8vs7kbm, sihyt /nt/0x gmpshght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite 55as epb3vnry-qs((z into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relativ5s(s rqn3 yz5- beap(ve to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencey:f .ji(fub70ok n8cb simulated g(fn87u k0o.c: ijybfbravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a ci:79jcxp nv 8x.juctm5rcular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellit9 8txvc 7xnm5j pjcu:.e?    s ~    min

  At what horizontal velocity would a satellite have to b+ cz t203m63m4 zpoupsx g: 8b:vfbpcme launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? p:m82vp +mmtbfz4pgx 3 uso6b03z c: c  

  During an Apollo lunar landing mission, the command module continued to orb5 p1-dy bux2mai9rxhks.1 t 1hit the Moon at an altir- ysmak 2p ixh 1tub5911x.dhtude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ao;4jqn0 gblx8zj+-wc(fhwu 9 re composed of chunks of ice that orbit the planet. The inner radiusxj8hq9g-0j4 bunw lozcf;+(w of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 j spxk/lug 1lc;g -xhp x))(8nm in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a pgs)pl8 1 x/h-;gk)xulxp(jncerson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrogzk 3w,ww7jkv)b/,h, *h zm cxnaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vz h xjkk7wchv)bw,z/gw,m,3 *elocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal ,d9fct6rb/iik l*z;g mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between t6d zc;firt/*lk b 9g,ihem. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womanm u 3-hz/1lldu.; yf emd31aqy in an elevator that / efh.;3ymqyz m -l1ld1udua3moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended f8+bdls jfv;*i (eycd3 b3 dv5c56nrfsrom the ceiling of an elevator. The cord can withst3dy5 s 5*ifcbsc+( fn8 jv3vb6el;d drand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planetxq +) q2*rfckj with period T , the density (mass/qcr*j fq+)2xk volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period qmb 7cn n+.jsf..9dny4jkct ,of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’smjf+n sj7 nd,n4. 9t qc.bkcy. surface.    s

  The asteroid Icarus, tq:b4p3f r):hgie(l cdhough only a few hundred meters across, orbits the Sun like the plaih cg )fbq3ldp :(:e4rnets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5t/j6mdl1l f. mwj5o 2l $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly onc1yufr b0,sk95 be2ugre every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum 2r95f,yb ker ubu10g sof the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of :pi/ i0lwn2o dthe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mashdmw.q*+/d jxm c6p3csu6-jr s, period, and mean distance for the four largest moons of Jupsd jcmh-j 36wm 6+ xc/uprdq*.iter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and d;ddgwd y19/y listance of the Moon. 9yd1d/;wy ldg   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupisyst7y .o j(+mter’s moons, using Kepler’s third law. Use s y(s+omy. tj7the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter co17umeim8 *fignsists of many fragments (which some space scientists think came from a planet that once orbited the g1 i 8uiemm*f7Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction ta(t- 8fje133oh l;asl.ljxro mle describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earhx;3ljlfjaom.otl s3- e8( 1rth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc ep z83h7zo)wcr,+snc xj+hf 8(:j l zvfrom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can to8j vl)3f 8opecxzwn+ zhs(:7jrzh +c, lerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will t9asu*gax czp 4 8+c40pulq6 e7xjtz8j he acceleration of gravity be half what it is on the surfaa 9440xjt cxz88 p*7 alqcu zsue6jg+pce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a7r )l a8 3yv/dken.c5ohqh:1 ipyvrt igw94m2 mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they p :)3w .ghek vtocrrv/ pan7m8i1lyhy d459i2 qulling on one another?    $\times 10^2$

  Because the Earth rotz 6u-hm87mst yates once per day, the apparent acceleration of gravity at the equator - m67hs z8myutis slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from thd: zq2 4yb9c9dp:ferye Earth will a spacecraft traveling directly from the Earth to the Mcre:qz9dy2fd49b p :yoon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, buh5o c.6*b+3n:b e z+jh prp:rechy/zet when you stand on a bathroom scale in an elevator, it says yo rnhyzphj/ez. 3:cp r*:oce e+65h +bbur mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circ6;godnq n) vc3ular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diamdcgoq 3n6)v ;neter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in. ;gv8pq5xp;fk1 a atf a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of btb.d-t8a:zx a planet in terms of its radius r, the acceleration due to gravbttz:.8 baxd- ity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a stro8wa w2kh:8q-dtu p,xing) is deflected from the vertical by anq8w ht-,wpx:o2u k8 da angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is gc fqzlh; vdn(71d 4i.*0dsapbanked for a design speed of If the coefficient of static friction n4qid(dpg;7h c.1z sd v alf*0is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e 66vzsf-bus7a,5v mpo quator were p uas 6v7f6o5m -z,bsvapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apr l//dke.9 x ohcfupm;*/npe+art of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curvbhcyxov 9)o .-fvdl:v78;xrx e of radius 235 m. A lamp suspended from the ceiling swings out to an anglvcxyfodxrb87 ox h-9:. )vv ;le of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as masj3 uha7 -br 6t,y hq: j3is7 5gsn)usrqsy3/fnsive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a per -y/sr57gfja7:)h hb njrsu33u6st3qi,ny q sson would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelw47.6gf/ ebr,mmas8f63 9fjk75ej qdoxkqqt y massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thi,s j/k.gfdx76jref 7k895 4w 3 bqoqmq6tfames by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traver1hs1 f luj::mfses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, fhusml1 1 ::fjand C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Posit1).*) du5x nxqj kifvoioning System (GPS) utilizes a group of 24 satellites orbiting the Earnvxu*jfx) 5d q)oi1.kth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvky-)e4l st yzuz;4ij ft.f7 y)ous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rzkzy4uy;)4sft-e fjt7 y.i)l oughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut -sqr eifa1,p yx)(jc pq7z1l4in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the saqy zcfx1r pe,pas17i (- q)l4jtellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean zq7;9 3vb,d / as kuj cnjnk0dbc089rldistance from the Sun? dj 9,zn9;0rk ub7k3d banv8q j/sc0lc  
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would nee 80.:b) pqt39yac mbm/sx tuewd to be if you could actually "feel" yourself gravitationally attracted to someone near you.8x t.:y pmuqbm9 aes/)btwc 30 Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4;tey595w wx ,bkedtk fs6-m( o6) at a distance of about 30ke sd6,kb-wo( m we559tx;yft,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each ajrsuigj-,bgrdz u51(djh4c; p,p4w 1ihk9 1side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom1 ;i4 sru g-bc9r1hwdup ji,,(hgk15j4ajpdz side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits theimvb .vhapygx9f8ch58, )v *l Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-l8n nd 1gmrp2vc1b 25ayong sweep second hand2c1 mrna1 5y2dp8n bgv on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sin2s rlv z2te4m7 +0pnesxy)t-oker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–107 mn )- yovz+2t4 spexr2tl0es.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trmcu w9fr k+0y)1 cqq a3g8pdq;3e 8xswaveling ys8gd xcpwkwur1m+e;0f39 qcqqa8)3 at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when ne.pyx5uinc(w*4 fu hb9 gotiating curves. The angle of tilt is adjusted so that the main force exeru5cwfypb u(* h.4 i9xnted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$